Letters

Beckham's Bend Badly Explained

I read the article "The Physics behind 'Bend it like Beckham' " in the July 2003 APS News.

This article repeats an explanation often given to nontechnical audiences about how lift is generated by airfoils and rotating spheres. However, the explanation has a serious flaw.

The article explains how the force on an object (ball or airfoil) is due to a combination of the force due to the pressure difference on the two sides of the object and the force due to the bending of the wake.

This is untrue.

At a microscopic level, the force on the object comes from the air molecules hitting it and changing their momentum. This is by definition pressure.

Since there is no action at a distance, the pressure distribution over the object accounts for all of the force on the object.

In a macroscopic continuum fluids picture, the force on the object is equal to the change in momentum of the fluid per unit time. The deflection of the wake is a change in momentum. Therefore, the deflection of the wake also accounts for all of the force on the object.

The pressure distribution and the bending of the wake are not separate effects. One is a direct consequence of the other.

You can't have a lift-generating pressure distribution without bending the flow, and vice-versa. Either one alone explains the force.